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<p>In the case that <span class="process-math">\({\bf A}\)</span> is real and symmetric, we have the following results:(a) The eigenvalues <span class="process-math">\(r_1, r_2, \cdots, r_n\)</span> are real (some of them may be the same).(b) Corresponding to <span class="process-math">\(r_1, r_2, \cdots, r_n\text{,}\)</span> there are <span class="process-math">\(n\)</span> linear independent and orthogonal eigenvectors <span class="process-math">\(\vec{\xi}^{(1)}, \vec{\xi}^{(2)}, \cdots, \vec{\xi}^{(n)}\)</span> ((<span class="process-math">\(\vec{\xi}^{(i)}, \vec{\xi}^{(j)})=0\text{,}\)</span> for <span class="process-math">\(i \neq j\)</span>).</p>
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